I not very good, just know basics lah.
just check from company firewall log can le. All they can see is IP address to and from only.
From there how they trace is depend on how they assign the IP to each computer is it physically assigned or is it thru DHCP.
If physically assigned of course can trace down to department and individual PC level lah. Of course can overcome this, First remember your own IP address, then after hours just grab anybody's to use and surf internet with it but remember to change back.
If DHCP means everytime you turn on your PC it grabs an IP from a pool of unused IP addresses maintained by a DHCP server. Today it may be this IP tomorrow maybe that, I dunno whether DHCP can trace or not, but so far never kanna caught leh
From outside www want to trace back to the source maybe check singnet or pacnet IP firewall logs lor. But if you surf out from using your company network, depending if your network admin kilat or not, if kilat admin normally they will configure out going IP traffic from company firewall will "hide" behind a fake IP, if buay heow administrator basically means die lah